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Turn-by-turn systems typically use an electronic voice to inform the user whether to turn left or right, the street name, and the distance to the next turn. [ 3 ] Mathematically, turn by turn navigation is based on the shortest path problem within graph theory , which examines how to identify the path that best meets some criteria (shortest ...
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs ...
Pursuit–evasion. Pursuit–evasion (variants of which are referred to as cops and robbers and graph searching) is a family of problems in mathematics and computer science in which one group attempts to track down members of another group in an environment. Early work on problems of this type modeled the environment geometrically. [1]
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently, a tournament is an orientation of an undirected complete graph. (However, as directed graphs, tournaments are not complete: complete directed graphs have two edges, in both directions, between ...
In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given size. It is one of the central results of extremal graph theory, an area studying the largest or smallest graphs with given properties, and is a special case of the forbidden subgraph problem on the maximum number of edges in a graph that ...
The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending ...
Result in combinatorics and graph theory. In mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and sufficientcondition for an object to exist: The combinatorialformulation answers whether a finitecollection of setshas a transversal ...
A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).
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